National University of Sciences & Technology (NUST)

School of Electrical Engineering and Computer Science (SEECS) Department of Electrical Engineering

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12mseenayub@seecs.edu.pkAnalysis of Stochastic Systems

Course Code: EE 801 Semester: Fall 2013

Credit Hours: 3+0 Prerequisite Codes: None

Instructor: Dr. Muhammad Usman Ilyas Class: MS-EE 5 (TECN and P&C)

Office: Room# A-312, SEECS Telephone: +92-51-9085-2133

Lecture Days: Tu 1530-1920h, We 1730-1620h E-mail: usman.ilyas@seecs.edu.pk

Class Room: CR-1 Consulting Hours: Thursday, 1700 to 1730Hrs

Knowledge Group: Networking, Communication Updates on LMS: Every Friday

Course Description: This course covers the fundamental tools of probabilistic modeling and random processes as they are useful for

communication, signal processing and control. The course introduces axiomatic definition of probability, set theory, conditional probability, permutations and combinations, random variables, distribution functions, probability density functions, mean, variance, characteristic functions, joint distributions, concepts of stochastic process, correlation and covariance, Poisson process, Markov chain and Markov process.

Books: Text Book: Alberto Leon-Garcia, Probability and Random Processes for Electrical Engineering, 2nd ed.,

Addison-Wesley..

Reference Books: 1. Sheldon Ross, Introduction to Probability Models, 9th ed., Academic Press, 2007. 2. Thomas M. Cover, Joy A. Thomas, Elements of Information Theory, Wiley Interscience,

1991. 3. Garnett P. Williams, Chaos Theory Tamed, Joseph Henry Press, 2001.

Main Topics to be Covered: The course spans over a number of different topics as under:

Introduction to Probability Theory (02 Week) Set Theory Mutual Exclusivity Conditional Probability Independence Random Variables (02 weeks) Probability and Cumulative Density Function Conditional pdf and cdf Expected Value and Variance Functions of Random Variables Transform Methods Multiple Random Variables (02 weeks) Independence of Multiple Random Variables Functions of MRVs Joint Probabilities Correlation Convergence Sum of Random Variables Limits and Inequalities (01 week) Central Limit Theorem

National University of Sciences & Technology (NUST)

School of Electrical Engineering and Computer Science (SEECS) Department of Electrical Engineering

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Markov and Chebyshev inequalities Stochastic Processes (03 weeks) Introduction to Random Processes Stationary Random Processes Continuity, Derivative, and Integral of Random Process Time Averaging Prediction, Estimation, Detection (03 weeks) Estimation Using Sample Mean Confidence Interval Maximum Likelihood Maximum a posteriori Probability Markov Chain and Processes (01 weeks) Introduction to Discrete and Continuous Markov Chains

Weightages:

Quizzes: 10%

Assignments: 15%

Midterm: 30%

Labs: 0%

Final Exam: 45%

Course Outcomes: Students will be able to apply different stochastic models to real world problems.

Grading Policy: Quiz Policy: There will be no retakes for quizzes Quizzes will be unannounced and normally last for 10-15

minutes. The question framed is to test the concepts involved in last lecture. It will be the instructors will to choose the number of quizzes for evaluations purposes. Grading for quizzes will be on a fix scale of 0 to 10. A score of 10 indicates an exceptional attempt towards the answer and a score of 1 indicates your answer is entirely wrong but you made a reasonable effort towards the solution. Scores in between indicate very good (8-9), good (6-7), satisfactory (4-5), and poor (2-3) attempt. Failure to make a reasonable effort to answer a question scores a 0.

Assignment Policy: In order to give practice and comprehensive understanding of subject, home assignments will be given. Late assignments will not be accepted / graded. All assignments will count towards the total (No best-of policy). The students are advised to do the assignment themselves. Copying of assignment is highly discouraged and taken as cheating case and will be forwarded for disciplinary action. The questions in assignment are more challenging to give students the confidence and extensive knowledge about the subject and enable them to prepare for the exams.

Lab Conduct: Not applicable

Plagiarism: SEECS maintains a strict no tolerance plagiarism policy. While collaboration in this course is highly encouraged, you must ensure that you do not claim other peoples work/ idea as your own. Plagiarism occurs when the words, ideas, assertions, theories, figures, images, programming codes of others is presented as your own work. You must cite and acknowledge

National University of Sciences & Technology (NUST)

School of Electrical Engineering and Computer Science (SEECS) Department of Electrical Engineering

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all sources of information in your assignments. Failing to comply with the SEECS plagiarism policy will lead to strict penalties including zero marks in assignments and report to the academic coordination office for disciplinary action.

Tools / Software Requirement: Matlab R2007